A Higher-Order Finite Difference Scheme for Singularly Perturbed Parabolic Problem

In this paper, we deal with a singularly perturbed parabolic convection-diffusion problem. Shishkin mesh and a hybrid third-order finite difference scheme are adopted for the spatial discretization. Uniform mesh and the backward Euler scheme are used for the temporal discretization. Furthermore, a p...

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Bibliographic Details
Published in:Mathematical problems in engineering 2021, Vol.2021, p.1-11
Main Authors: Tian, Shifang, Liu, Xiaowei, An, Ran
Format: Article
Language:English
Subjects:
Accuracy
Approximation
Convection-diffusion equation
Discretization
Finite difference method
Finite element analysis
Linear equations
Mathematical analysis
Preconditioning
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Summary:In this paper, we deal with a singularly perturbed parabolic convection-diffusion problem. Shishkin mesh and a hybrid third-order finite difference scheme are adopted for the spatial discretization. Uniform mesh and the backward Euler scheme are used for the temporal discretization. Furthermore, a preconditioning approach is also used to ensure uniform convergence. Numerical experiments show that the method is first-order accuracy in time and almost third-order accuracy in space.
ISSN:1024-123X
1563-5147
DOI:10.1155/2021/9941692